Just find ways to get involved that don't cost money. Go to reia groups, start talking to realtors, talk to a mortgage broker about getting pre qualified, call wholesalers from bandit signs, etc. Just start talking to as many people as possible and little by little the big picture will become clearer and clearer. Learn to ask good questions and find ways you can add value for the people you would like to learn from. Maybe even try to get a job in the industry so you can be close to it.
In the meantime get good at saving money, 5k is a great start. Sit down and work up a personal budget, run your personal finances like you would run a business, this is good practice. Figure out where you can reduce your expenses, strategically pay down high interest debt, and how much you can save every paycheck. For example many real estate investors would go out and risk their money to earn a 10% return. If you have debt that you are paying 10% on it maybe wise to pay it off.
I am not saying that deals haven't been done with 5k and a prayer but I think sometimes being in the right place at the right time has something to do with it. Unless you have a crystal ball you won't be able to predict the time, but you can put yourself in the right place by getting as close to the industry as possible via networking and some of the other things mentioned above. It's one of those things once you start on the path and stay on the path it's not that hard to hit your goals. It's may not be as fast as you would like but if you are consistent you can make anything happen.